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# Solve the trigonometric integral $\int\arctan\left(x\right)dx$

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e
π
ln
log
log
lim
d/dx
Dx
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θ
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sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

##  Final answer to the problem

$x\arctan\left(x\right)-\frac{1}{2}\ln\left|1+x^2\right|+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
Can't find a method? Tell us so we can add it.
1

Apply integration by parts: $u=arctan(x)$, $v'=1$

$x\arctan\left(x\right)-\int\frac{x}{1+x^2}dx$

Learn how to solve trigonometric integrals problems step by step online.

$x\arctan\left(x\right)-\int\frac{x}{1+x^2}dx$

Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(arctan(x))dx. Apply integration by parts: u=arctan(x), v'=1. The integral -\int\frac{x}{1+x^2}dx results in: -\frac{1}{2}\ln\left|1+x^2\right|. Gather the results of all integrals. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

##  Final answer to the problem

$x\arctan\left(x\right)-\frac{1}{2}\ln\left|1+x^2\right|+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.